evolution - What do we know about the Last Universal Common Ancestor (LUCA)?

Carl Woese has much to say on this subject, including:

“The ancestor cannot have been a particular organism, a single
organismal lineage. It was communal, a loosely knit, diverse
conglomeration of primitive cells that evolved as a unit, and it
eventually developed to a stage where it broke into several distinct
communities, which in their turn become the three primary lines of
descent [bacteria, archaea and eukaryotes].”

There is a 2000 Scientific American article by W.F. Doolittle that discusses much of Woese's (and others') work understanding this question.

Also, see a couple of Woese articles here and here.